Alignment of defect levels and band edges through hybrid functionals: Effect of screening in the exchange term

We investigate how various treatments of exact exchange affect defect charge transition levels and band edges in hybrid functional schemes for a variety of systems. We distinguish the effects of long-range vs short-range exchange and of local vs nonlocal exchange. This is achieved by the consideration of a set of four functionals, which comprise the semilocal Perdew-Burke-Ernzerhof (PBE) functional, the PBE hybrid (PBE0), the Heyd-Scuseria-Ernzerhof (HSE) functional, and a hybrid derived from PBE0 in which the Coulomb kernel in the exact exchange term is screened as in the HSE functional but which, unlike HSE, does not include a local expression compensating for the loss of the long-range exchange. We find that defect levels in PBE0 and in HSE almost coincide when aligned with respect to a common reference potential, due to the close total-energy differences in the two schemes. At variance, the HSE band edges determined within the same alignment scheme are found to shift significantly with respect to the PBE0 ones: the occupied and the unoccupied states undergo shifts of about +0.4 eV and -0.4 eV, respectively. These shifts are found to vary little among the materials considered. Through a rationale based on the behavior of local and nonlocal long-range exchange, this conclusion is generalized beyond the class of materials used in this study. Finally, we explicitly address the practice of tuning the band gap by adapting the fraction of exact exchange incorporated in the functional. When PBE0-like and HSE-like functionals are tuned to yield identical band gaps, their respective results for the positions of defect levels within the band gap and for the band alignments at interfaces are found to be very close.

Band alignment at the CaF2/Si(111) interface through advanced electronic structure calculations

Thomas Bischoff, Alfredo Pasquarello, Igor Reshetnyak

We determine the band alignment at the CaF2/Si(111) interface through various advanced electronic structure methods. This interface is experimentally well studied and serves as an ideal test case to examine the accuracy of theoretical schemes. We use both global and range-separated hybrid functionals as well as GW calculations including self-consistency and vertex corrections. Our calculation procedure accounts for residual strain resulting from the small mismatch in the lateral lattice constants at the interface to minimize the systematic error in the comparison with experiment. Both the hybrid functional and the GW schemes give band alignments in overall good agreement with the experimental characterization. However, the considered methods yield sizable variations in the calculated band offsets, which do not originate from incorrect evaluations of the band gaps but rather from different inherent relative positions of the band edges. The comparison with experiment reveals that the global hybrid functional and the quasiparticle self-consistent GW with vertex corrections give the most accurate description of the band alignment. We then determine the variation of the band offsets as a function of the amount of excess fluorine at the interface and attribute the experimental spread in the measured offsets to uncontrolled fluorine contamination.

AMER PHYSICAL SOC2020

Nonempirical hybrid functionals for advanced electronic-structure calculations

Thomas Bischoff

Electronic-structure calculations based on hybrid functionals have emerged as a standard technique used in physics, chemistry, and material science. Despite this success, hybrid functionals have the drawback of containing undetermined parameters. To overcome this deficiency, two different nonempirical determination schemes are being investigated at present, namely dielectric-dependent hybrid (DDH) functionals and hybrid functionals that satisfy Koopmans' condition. This thesis is dedicated to the examination and further development of these approaches. In particular, we show that a precise description of band gaps in condensed-matter systems can be achieved with these functionals. Moreover, we demonstrate that their accuracy is comparable to state-of-the-art

GW

methods while requiring substantially lower computational cost. First, we focus on the development of hybrid functionals satisfying Koopmans' condition. We show that the construction of those functionals can be optimized through suitably defined potential probes. By monitoring the delocalized screening charge, we achieve a measure of the degree of hybridization with the band states, which can be used to improve the band-gap estimate. We show that the application of this methodology to common semiconducting and insulating materials yields band gaps differing by less than 0.2 eV from experiment. These conceptual developments are an important step towards establishing hybrid functionals satisfying Koopmans' condition as a robust approach for band-gap predictions. Second, we examine DDH functionals and hybrid functionals satisfying Koopmans' condition for band gaps of more sophisticated materials. In particular, we focus on inorganic metal-halide perovskites which have recently drawn great scientific attention. For this class of materials, we show that both nonempirical hybrid-functional schemes yield band gaps of comparable accuracy (

\sim

0.2 eV) with respect to

GW

reference calculations. Furthermore, we discuss the suitability of nonempirical hybrid-functional schemes for the application to the screening of large sets of perovskite materials. Third, we investigate the fundamental band gap of liquid water and hexagonal ice. These materials are particularly challenging since experimental studies have not reached a consensus on the band gap yet. Therefore, we first deduce robust benchmarks on the basis of a critical review of various experimental studies in the literature. Then, we compute the band gap through state-of-the-art

GW

methods as well as nonempirical hybrid functionals. We show that theoretical calculations and experimental references are in good agreement with each other and we discuss critical aspects which are essential to ensure a consistent description of the band gap. Finally, we investigate band-edge levels as obtained with hybrid-functional calculations. The CaF

_2

/Si(111) interface serves thereby as an ideal test case to examine the accuracy of different theoretical schemes. The comparison with experiment reveals that global hybrid functionals and self-consistent

GW

methods provide the most accurate description of the interfacial band alignment.

EPFL2021

First-principles study of defects at the SiC/SiO2 interface through hybrid functionals

Fabien Devynck

The requirements of present high-performance power electronic systems are exceeding the power density, efficiency, and reliability of silicon-based devices. Silicon carbide (SiC) is a candidate of choice for high-temperature, high-speed, high-frequency, and high-power applications: it has a wide band gap, high thermal conductivity, high saturated electron drift velocity, and high breakdown electric field. SiC is also hard, chemically stable, and resistant to radiation damage. Despite these desirable electronic properties, SiC-based devices are still facing many performance challenges due to the high density of defect states at the SiC/SiO2 interface. This thesis is dedicated to the first-principles study of defects at the SiC/SiO2 interface through hybrid functionals. We first generate a model structure providing a realistic description of the majority bonding arrangements at the 4H(0001)-SiC/SiO2 interface. The description of the electronic structure of the model through hybrid functionals leads to band offsets in excellent agreement with their experimental counterparts. We then study several semiconductor and oxide defects using spin-polarized hybrid density functionals and identify candidate defects responsible for the high density of interface defects measured in the 4H-SiC band gap. Finally, the possibility of growing epitaxial silicate adlayers on SiC is investigated as an alternative approach to greatly reduce the high density of defect states at the SiC/SiO2 interface.

EPFL2008

Nonempirical hybrid functionals for advanced electronic-structure calculations

Thomas Bischoff

GW

\sim

0.2 eV) with respect to

GW

GW

_2

GW

methods provide the most accurate description of the interfacial band alignment.

EPFL2021